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  • Level: GCSE
  • Subject: Maths
  • Word count: 3452

T-Total Maths

Extracts from this document...

Introduction

Atif Eshaque Kamal                                                                                

T-TOTAL

INTRODUCTION

In this coursework. I will be investigating the difference between T-Total and T-number. I am going to do this by doing different grids and in different angles. Then I will compare them to see the difference and what is common in each one of them .I am going to draw a T-shape inside the grid. The number, which will be at the bottom on T, is called T-Number. Counting all the numbers inside T will give T-Total. I am going to show you by drawing grid and plotting which is T-Total and T-Number.

ALL THE NUM

        IN THE T ARE

        T-TOTAL

        THIS IS T-NUMBER

INVESTIGATION

I am going to be investigating the grids and the T-shape inside the grid. Which I have drawn underneath. The things I will be investigating and finding out are the formula for each of the grid and checking the pattern and what is common things in the formula of each of the grid. I will also find the algebraic way of working the formula. Lastly I will move the T-Shape in different angles.

The grids below will help me in my investigation. From these grids I will find the pattern of the formulas and a common formula that goes in every grid which l have done below.

GRIDS – 5

T NUMBER

T-TOTAL

12

25

13

30

14

35

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

12

1

2

3

7

13

2

3

4

8

14

3

4

5

9

Numbers inside Tshape

T NUMBER

T TOTAL

14

28

15

33

16

38

17

43

5 X 12 = 60 – 25

= 35

FORMULA

= 5N - 35

GRID-6

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

Numbers inside T shape

14

1

2

3

8

15

2

3

4

9

16

3

4

5

10

17

4

5

6

11

5 X 14 = 70 – 28

= 42

FORMULA

= 5N - 42

GRID 7

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

39

40

41

42

43

43

44

45

46

47

48

49

T NUMBER

T TOTAL

16

31

17

36

18

41

19

46

20

57

Numbers inside T shape

16

1

2

3

9

17

2

3

4

10

18

3

4

5

11

19

4

5

6

12

20

5

6

7

13

5 X 16 = 80 – 39

= 49

FORMUAL

=5N - 49

GIRD-8

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

49

50

52

53

54

55

56

57

58

59

60

61

62

53

64

T NUMBER

T TOTAL

18

34

19

39

20

44

21

49

22

54

23

59

Numbers inside T shape

18

1

2

3

10

19

2

3

4

11

20

3

4

5

12

21

4

5

6

13

22

5

6

7

14

23

6

7

8

15

5 X 18 = 90 – 34

= 56

FORMULA

= 5N – 56

GRID-9

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63

64

65

66

67

68

69

70

71

72

73

74

75

76

77

78

79

80

81

T NUMBER

T TOTAL

20

37

21

42

22

47

23

52

24

57

25

62

26

67

Numbers inside T shape

20

11

1

2

3

21

12

2

3

4

22

13

3

4

5

23

14

4

5

6

24

15

5

6

7

25

16

6

7

8

26

17

7

8

9

5 X 20 = 100 – 37

= 63

FORMUAL

5N – 63

GRID-10

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63

64

65

66

67

68

69

70

71

72

73

74

75

76

77

78

79

80

81

81

82

83

...read more.

Middle

18

13

12

14

FORMULA USING

5N – 35

5 X 23 = 115 – 80

= 35

GRID 6

T NUMBER

T TOTAL

28

98

28

22

15

16

17

FORMULA USING

5N – 42

5 X 28 = 140 – 98

= 42

GRID 7

T NUMBER

T TOTAL

39

149

39

32

24

25

26

FORMULA USING

5N – 49

5 X 93 = 195 – 146

= 49

GRID 8

T NUMBER

T TOTAL

54

214

54

46

37

38

39

FORMULA USING

5N – 56

5 X 54 = 270 – 214

= 56

T NUMBER

T TOTAL

59

232

GRID 9

59

50

40

41

42

FORMULA USING

5N – 63

5 X 59 = 295 – 232

= 63

GRID 10

T NUMBER

T TOTAL

76

310

76

66

56

55

57

FORMULA USING

5N – 70

5 X 76 = 380 – 310

= 70

I have done the checking and it shows that I have put in the correct formula that goes in each grid.

I am going to investigate the pattern in formula and find the common number from the grids formula. Below are the T-Number and T-Total and the numbers.

GRIDS – 5

T NUMBER

T-TOTAL

12

25

13

30

14

35

Numbers inside T shape

12

1

2

3

7

12

13

2

3

4

8

13

14

3

4

5

9

14

5 X 12 = 60 – 25

= 35

FORMULA

= 5N - 35

T NUMBER

T TOTAL

14

28

15

33

16

38

17

43

GRID-6

Numbers inside T shape

14

1

2

3

8

14

15

2

3

4

9

15

16

3

4

5

10

16

17

4

5

6

11

17

5 X 14 = 70 – 28

= 42

FORMULA

= 5N - 42

GRID 7

T NUMBER

T TOTAL

16

31

17

36

18

41

19

46

20

57

Numbers inside T shape

16

1

2

3

9

17

2

3

4

10

18

3

4

5

11

19

4

5

6

12

20

5

6

7

13

5 X 16 = 80 – 39

= 49

FORMUAL

=5N - 49

GIRD-8

Numbers inside T shape

T NUMBER

T TOTAL

18

34

19

39

20

44

21

49

22

54

23

59

18

1

2

3

10

19

2

3

4

11

20

3

4

5

12

21

4

5

6

13

22

5

6

7

14

23

6

7

8

15

5 X 18 = 90 – 34

= 56

FORMULA

= 5N – 56

T NUMBER

T TOTAL

20

37

21

42

22

47

23

52

24

57

25

62

26

67

GRID-9

Numbers inside T shape

20

11

1

2

3

21

12

2

3

4

22

13

3

4

5

23

14

4

5

6

24

15

5

6

7

25

16

6

7

8

26

17

7

8

9

5 X 20 = 100 – 37

= 63

FORMUAL

= 5N – 63

T NUMBER

T TOTAL

22

40

23

45

24

50

25

55

26

60

27

65

28

70

29

75

GRID 10

Numbers inside T shape

22

1

2

3

12

23

2

3

4

13

24

3

4

5

14

25

4

5

6

15

26

5

6

7

16

27

6

7

8

17

28

7

8

9

18

29

8

9

10

19

 5 X 22 = 110 – 40

=70

FORMULA

=5N – 70

FORMULAS

GRID 5     = 5N - 35

GRID 6     = 5N - 42

GRID 7      =5N - 49

GRID 8       = 5N – 56

GRID 9       = 5N – 63

GRID 10      =5N – 70

PATTERN =35, 42, 49, 56, 63, 70

This shows that is it going up by 7 and it a multiple of 7.

COMMON = 5N because they all start with 5N and it the difference is 5 as well.

All the grids above formula begin with 5N because that how many numbers inside the T-shape. Number 7 links the endings of each formula because all the grids I have done its T-Total are multiples of 7.it also gives me the last part of the formula. Which I shown above.

FORMULA THAT GOES IN EACH GRID

I have found the formula that will help me find T-Total of any grid.

FORMULA = 5N – 7W

(N = T NUMBER)

(W = WIDTH OF GRID)

I will show you working out of each grid using the formula above, which will give me the T-Total of any grid.

WORKING OUT: -

GRID - 5         

5 X 14 = 70

7 X 6 = 42

70 – 42

T-TOTAL = 25

GRID - 6

5 X 14 = 70

7 X 6 = 42

70 – 42

T-TOTAL = 28

GRID 7

5 X 16 = 80

7 X 7 = 49

80 – 49

T-TOTAL = 31

GRID 8

5 X 18 = 90

7 X 8 = 42

90 – 42

T-TOTAL = 34

GRID 9

5 X 20 = 100

7 X 9 = 63

100 – 63

T-TOTAL = 37

GRID 10

5 X 22 = 110

7 X 10 = 70

110 – 70

T-TOTAL = 40

As you can see above. That my calculation prove that I have found the

T-Total of any number using the formula (5N – 7W).

MOVING THE T UPSIDEDOWN

GRIDS – 5

T NUMBER

T-TOTAL

2

45

3

50

4

55

Numbers inside T shape

2

7

11

12

13

3

8

12

13

14

4

9

13

14

15

5 X 2 = 10 – 45

= - 35

FORMULA

= 5N + 35

GRID-6

T NUMBER

T TOTAL

2

52

3

57

4

62

5

67

Numbers inside T shape

2

8

13

14

15

3

9

14

15

16

4

10

15

16

17

5

11

16

18

19

5 X 2 = 10 – 52

= - 42

FORMULA

= 5N + 42

GRID 7

T NUMBER

T TOTAL

2

59

3

64

4

69

5

74

6

79

Numbers inside T shape

2

9

15

16

17

3

10

16

17

18

4

11

17

18

19

5

12

18

19

20

6

13

17

20

21

5 X 2 = 10 – 39

= - 49

FORMUAL

=5N + 49

GIRD-8

Numbers inside T shape

T NUMBER

T TOTAL

2

66

3

71

4

76

5

81

6

86

7

91

2

10

17

18

19

3

11

18

19

20

4

12

19

20

21

5

13

20

21

22

6

14

21

22

23

7

15

22

23

24

5 X 2 = 10 – 66

= - 56

FORMULA

= 5N + 56

GRID-9

T NUMBER

T TOTAL

2

73

3

78

4

83

5

88

6

93

7

98

8

103

Numbers inside T shape

2

11

19

20

21

3

12

20

21

22

4

13

21

22

23

5

14

22

23

24

6

15

23

24

25

7

16

24

25

26

8

17

25

26

27

5 X 2 = 10 – 73

= - 63

FORMUAL

= 5N + 63

GRID-10

T NUMBER

T TOTAL

2

80

3

85

4

90

5

95

6

100

7

105

8

110

9

115

...read more.

Conclusion

GRID 9

N + N-1 - N-2 – N-11 + N+7 (FORMULA=5N-7)

GRID 10

N + N-1 - N-2 – N-12 + N+8 (FORMULA=5N-7)

TURNING T RIGHT

GRID 5

N + N+1 + N+2 + N+7 – N-3 (FORMULA=5N+7)

GRID 6

N + N+1 + N+2 + N+8 – N-4 (FORMULA=5N+7)

GRID 7

N + N+1 + N+2 + N+9 – N-5 (FORMULA=5N+7)

GRID 8

N + N+1 + N+2 + N+10 – N-6 (FORMULA=5N+7)

GRID 9

N + N+1 + N+2 + N+11 – N-7 (FORMULA=5N+7)

GRID 10

N + N+1 + N+2 + N+12  - N-8 (FORMULA=5N+7)

 In the grids above I have used algebra in the T shape to show that I can do working out in algebraic form. The difference was that T shape was + (positive) and when T shape was turned upside-down was – (negative).

When I turned T shape left and then right I found the formula that goes into both of the shapes was 5n-7.the only differences was that T shape which was turn left had a – (Negative) and the one turned was + (positive).

FINDING THE W BY W GRID

T SHAPE

N – N-W – N-2W – N-2W-1 – N-2W+1

TURNING T UPSIDE DOWN

N+ N+W + N+2W + N+2W+1 + N+2W-1

I have found that T shape and upside-down shape have the same w-by w formula that will give 5n-7w.Doing that formula I can work out and any number when I draw T shape and when I turn it up side down.

TURNING T LEFT

 N + N-1 + N-2 + N+2+W + N-2+W

TURNING T RIGHT

 N + N+1 + N+2  + N+2 – W + N+2+W

...read more.

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